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S-stability properties for generalized Runge-Kutta methods. (English) Zbl 0336.65036


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
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References:

[1] Dahlquist, G. G.: A special stability problem for linear multistep methods, BIT3, 27-43 (1963) · Zbl 0123.11703
[2] Enright, W. H., Hull, T. E., Lindberg, B.: Comparing numerical methods for stiff systems of ODEs, Techn. Report No. 69, Dept. of Comp. Sc, University of Toronto (1974) · Zbl 0301.65040
[3] Lambert, J. D.: Computational methods in ordinary differential equations. London: John Wiley and Sons 1973 · Zbl 0258.65069
[4] Prothero, A., Robinson, A.: On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations. Math. Comp.28, 145-162 (1974) · Zbl 0309.65034
[5] Rosenbrock, H. H.: Some general implicit processes for the numerical solution of differential equations. Comput. J.5, 329-330 (1963) · Zbl 0112.07805
[6] Van der Houwen, P. J.: Explicit and semi-implicit Runge-Kutta formulas for the integration of stiff equations. Report TW 132, Mathematisch Centrum, Amsterdam (1972) · Zbl 0285.65047
[7] Van der Houwen, P. J.: Construction of integration formulas for initial value problems. Amsterdam: North-Holland Publishing Company 1976 · Zbl 0359.65057
[8] Van Veldhuizen, M.: Convergence of one-step discretizations for stiff differential equations (Thesis), Mathematical Institute, University of Utrecht, Netherlands (1973)
[9] Verwer, J. G.:S-stability and stiff-accuracy for two classes of generalized integration methods. Report NW 15/75, Mathematisch Centrum, Amsterdam (1975) · Zbl 0306.65045
[10] Verwer, J. G.: InternalS-stability for generalized Runge-Kutta methods. Report NW, 21/75, Mathematisch Centrum, Amsterdam (1975) · Zbl 0319.65044
[11] Verwer, J.G.: On generalized linear multistep methods with zeroparasitic roots and adaptive principal root. Numer. Math.,27, 143-155 (1977) · Zbl 0326.65045
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